{"id":"https://openalex.org/W3174324873","doi":"https://doi.org/10.3390/sym13061095","title":"New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations","display_name":"New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations","publication_year":2021,"publication_date":"2021-06-21","ids":{"openalex":"https://openalex.org/W3174324873","doi":"https://doi.org/10.3390/sym13061095","mag":"3174324873"},"language":"en","primary_location":{"id":"doi:10.3390/sym13061095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061095","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1095/pdf?version=1624515057","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/6/1095/pdf?version=1624515057","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074973583","display_name":"Osama Moaaz","orcid":"https://orcid.org/0000-0003-3850-1022"},"institutions":[{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["EG","IT"],"is_corresponding":true,"raw_author_name":"Osama Moaaz","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019347203","display_name":"Belgees Qaraad","orcid":"https://orcid.org/0000-0002-2115-0791"},"institutions":[{"id":"https://openalex.org/I4210160302","display_name":"Amran University","ror":"https://ror.org/055y2t972","country_code":"YE","type":"education","lineage":["https://openalex.org/I4210160302"]},{"id":"https://openalex.org/I159247623","display_name":"Mansoura University","ror":"https://ror.org/01k8vtd75","country_code":"EG","type":"education","lineage":["https://openalex.org/I159247623"]}],"countries":["EG","YE"],"is_corresponding":false,"raw_author_name":"Belgees Qaraad","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Amran University, Amran 999101, Yemen","Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Amran University, Amran 999101, Yemen","institution_ids":["https://openalex.org/I4210160302"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt","institution_ids":["https://openalex.org/I159247623"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091855471","display_name":"Nawal A. Alshehri","orcid":"https://orcid.org/0000-0002-8373-1428"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Nawal A. Alshehri","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041270026","display_name":"S.K. Elagan","orcid":"https://orcid.org/0000-0003-4781-5445"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Sayed K. Elagan","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060547119","display_name":"Mohammed Zakarya","orcid":"https://orcid.org/0000-0003-4312-8330"},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]},{"id":"https://openalex.org/I82952536","display_name":"King Khalid University","ror":"https://ror.org/052kwzs30","country_code":"SA","type":"education","lineage":["https://openalex.org/I82952536"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mohammed Zakarya","raw_affiliation_strings":["Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia","institution_ids":["https://openalex.org/I82952536"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5074973583","https://openalex.org/A5080017749"],"corresponding_institution_ids":["https://openalex.org/I159247623","https://openalex.org/I4210155399"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.1506,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.85488308,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"13","issue":"6","first_page":"1095","last_page":"1095"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/oscillation","display_name":"Oscillation (cell signaling)","score":0.737897515296936},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.7034816145896912},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.6538477540016174},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.6516671180725098},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5846315622329712},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.579406201839447},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5698232054710388},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.525830864906311},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.4653658866882324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46454381942749023},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4157610237598419},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3887542486190796},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2969030737876892},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27889907360076904},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.14401111006736755},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.048810333013534546}],"concepts":[{"id":"https://openalex.org/C2778439541","wikidata":"https://www.wikidata.org/wiki/Q7106412","display_name":"Oscillation (cell signaling)","level":2,"score":0.737897515296936},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.7034816145896912},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6538477540016174},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.6516671180725098},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5846315622329712},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.579406201839447},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5698232054710388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.525830864906311},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.4653658866882324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46454381942749023},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4157610237598419},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3887542486190796},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2969030737876892},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27889907360076904},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.14401111006736755},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.048810333013534546},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13061095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061095","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1095/pdf?version=1624515057","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:2d65cbcd794645d2928fa0e58ed92247","is_oa":true,"landing_page_url":"https://doaj.org/article/2d65cbcd794645d2928fa0e58ed92247","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 6, p 1095 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/1095/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13061095","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13061095","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061095","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1095/pdf?version=1624515057","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3174324873.pdf","grobid_xml":"https://content.openalex.org/works/W3174324873.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W572159918","https://openalex.org/W1972565057","https://openalex.org/W1982544530","https://openalex.org/W2002667813","https://openalex.org/W2003632449","https://openalex.org/W2006505167","https://openalex.org/W2017273183","https://openalex.org/W2020155377","https://openalex.org/W2034991404","https://openalex.org/W2043064520","https://openalex.org/W2067637036","https://openalex.org/W2079871064","https://openalex.org/W2120201283","https://openalex.org/W2740471416","https://openalex.org/W3012682553","https://openalex.org/W3042808435","https://openalex.org/W6654666093","https://openalex.org/W6677705944","https://openalex.org/W6780921033"],"related_works":["https://openalex.org/W2390991069","https://openalex.org/W2348576774","https://openalex.org/W3210114745","https://openalex.org/W2362061707","https://openalex.org/W2150987529","https://openalex.org/W2352047463","https://openalex.org/W2386228494","https://openalex.org/W2073949697","https://openalex.org/W2043753575","https://openalex.org/W2549420386"],"abstract_inverted_index":{"Differential":[0],"equations":[1,13,33,79],"with":[2],"delay":[3,66],"arguments":[4],"are":[5],"one":[6],"of":[7,10,31,36,50,60,63,77],"the":[8,18,32,48,57],"branches":[9],"functional":[11],"differential":[12,67],"which":[14],"take":[15],"into":[16],"account":[17],"system\u2019s":[19],"past,":[20],"allowing":[21],"for":[22,74],"more":[23],"accurate":[24],"and":[25,38,44,88],"efficient":[26],"future":[27],"prediction.":[28],"The":[29,83],"symmetry":[30],"in":[34,47],"terms":[35],"positive":[37],"negative":[39],"solutions":[40,76],"plays":[41],"a":[42,61],"fundamental":[43],"important":[45],"role":[46],"study":[49,56],"oscillation.":[51],"In":[52],"this":[53],"paper,":[54],"we":[55],"oscillatory":[58],"behavior":[59],"class":[62],"odd-order":[64],"neutral":[65],"equations.":[68],"We":[69],"establish":[70],"new":[71],"sufficient":[72],"conditions":[73],"all":[75],"such":[78],"to":[80],"be":[81],"oscillatory.":[82],"obtained":[84],"results":[85],"improve,":[86],"simplify":[87],"complement":[89],"many":[90],"existing":[91],"results.":[92]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
